184 TERMINOLOGY. . 



becomes the character by which it is possible to ascertain 

 whether or not a form of several axes belongs to the com- 

 pass of those which may be derived immediately from the 

 hexahedron. All these fonns are contained under the first 

 degree of regularity (. 47.). 



If, instead of a rhombohedron, we substitute the hexa- 

 hedron, or, instead of an isosceles four-sided pyramid the oc- 

 tahedron, and apply to them the modes of derivation describ- 

 ed above (. 80. 81. 82.) : certain combinations between the 

 derived forms will likewise represent the whole compass of 

 those obtained by the process of the moveable plane ; some 

 of them even with their determined dimensions, which may 

 be considered as an advantage of this method. It requires, 

 however, some knowledge of compound forms (. 34.), 

 upon the resolution or developement of which it depends. 



The designation of the forms of several axes has been 

 framed upon a principle different from that followed in the 

 designation of the rest of simple forms. The great num- 

 ber of distinct kinds of forms, and the few varieties of each, 

 known or occurring in the compass of derived forms, have 

 been the reason why it was impossible to trace in the crys- 

 tallographic signs, all those relations of the forms to each 

 other which distinguish the designation of the fonns 

 derived from the four-sided pyramids and from the rhom- 

 bohedrons. The following method, although it does not 

 possess the advantage of expressing these relations, yet 

 is recommended by its brevity and distinctness. 



Designate the hexahedron by the letter H, the octahe- 

 dron by O, the dodecahedron by D, the tetracontaoctahe- 

 dron by T ; these being the initial letters of their respec- 

 tive names. The initial letters of the icositetrahedrona 

 cannot be employed in the same way, because there are 

 three different kinds of such forms among those immediate- 

 ly derived from the hexahedron ; namely, the hexahe- 

 dral and the octahedral trigonal-icositetrahedrons, and the 

 digrammic tetragonal-icositetrahedron. Designate the first 

 of these by A, the second by B, the third by C ; and add 

 . to them, as Avell as to the sign of the tetracontaoctahedrons , 



